This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 11-271260, filed Sep. 24, 1999, the entire contents of which are incorporated herein by reference.
The present invention relates to an aberration measuring method, an aberration measuring system and an aberration measuring mask for measuring a lens aberration in an optical system.
A lens aberration of an exposure apparatus used in a lithography process adversely affects a pattern position error, a focus error, a variation in pattern dimensions on a semiconductor device pattern. The kind of aberration can be determined, depending on whether the effect of the lens aberration relates to the pattern size or the pattern direction.
Conventional methods of evaluating astigmatism or spherical aberration using such phenomena include a Kirk method (Joseph P. Kirk, xe2x80x9cAstigmatism and field curvature from pinbarsxe2x80x9d, SPIE Vol. 1463 (1991), P.294), a line-width abnormality value measuring method which evaluates coma aberration, and a relative displacement measuring method (Jpn. Pat. Appln. KOKAI Publication No. 11-142108).
FIGS. 1A to 1D show aberration measuring patterns used in the line-width abnormality value measuring method. In the line-width abnormality value measuring method, five line patterns each with an equal line width, as shown in FIGS. 1A to 1D, are transferred on a wafer, and an error in line width between both endmost lines is measured by a length-measuring type scanning electron microscope (SEM). As is shown in FIGS. 1A to 1D, four five-line patterns having line directions set at 0xc2x0, 45xc2x0, 90xc2x0 and 135xc2x0 with respect to a reference straight line 111 are provided, thereby to measure aberration in each line-width direction.
FIGS. 2A and 2B show aberration measuring patterns used in the relative displacement measuring method. In the relative displacement measuring method, as shown in FIGS. 2A and 2B, two kinds of patterns with different line widths are disposed in parallel, and a relative displacement is measured by using a difference in positional displacement of each pattern width. Based on the amount of the relative displacement, an aberration is measured. The pattern shown in FIG. 2A is used to measure an aberration in 0xc2x0 and 90xc2x0 directions with respect to a reference line 121, and the pattern shown in FIG. 2B is used to measure an aberration in 45xc2x0 and 135xc2x0 directions with respect to the reference line 121.
With further reduction in pattern size and variation in device structure in modern technology, there arise problems of aberrations other than coma aberration. For instance, in fabrication of DRAMs, capacitors with deep trench structure have been formed. Unlike conventional line and space patterns, etc., the deep-trench type capacitor has a two-dimensional pattern. Specifically, a pattern is disposed in one direction, and another pattern is disposed in another direction. In this case, it is necessary to consider not only the effect of the pattern disposed in one direction, but also the relationship among the patterns disposed in a plurality of directions, in particular, a diffraction. Also in the case of device activation regions, etc. there is the same necessity to consider the relationship among the patterns disposed in a plurality of directions.
Specifically, in the conventional line and space pattern, etc., the sizes of patterns disposed in one direction will vary due to diffraction. This adverse effect has been observed in the prior art. In order to decrease it, a method has been proposed wherein an aberration in a projecting optical system is measured and corrected and thus a normal pattern is formed. With this aberration measurement, adequate pattern precision has been obtained in the conventional patterns.
On the other hand, in the case of the deep-trench capacitor, for instance, diffraction occurs not only between adjacent patterns disposed in one direction but also between adjacent patterns disposed in plural directions. Consequently, transferred patterns become triangular or pentagonal. It is known that this undesirable phenomenon is due to an aberration called xe2x80x9cthree-fold symmetry aberrationxe2x80x9d or xe2x80x9cfive-fold symmetry aberrationxe2x80x9d occurring in the projecting optical system.
It is known that each term of a Zernike series obtained by series-developing a Zernike function, which is obtained by expressing the lens aberration function by the function of coordinates (R, xcex8) at a pupil plane, is represented by a radial function (zernike coefficient ZIxc3x97variable R). For instance, the term representing coma aberration is expressed by Z2R cos xcex8, Z3Rsinxcex8; the term representing three-fold symmetry aberration is expressed by Z10R3 cos 3xcex8, Z11R3 sin 3xcex8; and the term representing five-fold symmetry aberration is expressed by Z26R5 cos 5xcex8, Z27R5 sin 5xcex8.
There are conventional aberration measurement methods for measuring an aberration between an axial direction, and a direction perpendicular thereto, or between the axial direction and a direction at 45xc2x0 or 135xc2x0 thereto. However, there is no methods of measuring other aberrations. In the case of conventionally fabricated patterns, adequate pattern precision and exposure tolerance have been obtained without the need to measure such other aberrations. By contrast, in the case of modern small-sized patterns, adequate pattern precision and exposure tolerance cannot be obtained.
The object of the present invention is to provide an aberration measuring method, an aberration measuring system and an aberration measuring mask capable of measuring an (2n+1)-fold (n=natural number) symmetry aberration.
According to an aspect of the present invention, there is provided an aberration measuring method comprising the steps of providing an aberration mask comprising a plurality of aberration measuring pattern units each having a plurality of elemental patterns arranged in a direction of a given straight line, the aberration measuring pattern units being disposed in a given circumferential direction such that the straight line of each of the aberration measuring pattern units is cyclically shifted relative to a reference line at an angle of (xcfx80/2)/(2n+1) rad (n=natural number) in a range between 0 rad and xcfx80/2 rad; transferring pattern images of the aberration measuring mask onto a substrate to be processed, using an optical system; and detecting the transferred pattern image, thereby measuring an aberration in the direction of the reference straight line of the optical system.
According to another aspect of the invention, there is provided an aberration measuring system comprising an illumination optical system; an aberration measuring mask disposed on an optical path of light from the illumination optical system and comprising a plurality of aberration measuring pattern units each having a plurality of elemental patterns arranged in a direction of a given straight line, the aberration measuring pattern units being disposed in a given circumferential direction such that the straight line of each of the aberration measuring pattern units is cyclically shifted relative to a reference line at an angle of (xcfx80/2)/(2n+1) rad (n=natural number) in a range between 0 rad and xcfx80/2 rad; and a projecting optical system for focusing light, which has passed through the aberration measuring mask, onto a substrate to be processed.
According to still another aspect of the invention, there is provided an aberration measuring mask comprising a plurality of aberration measuring pattern units each having a plurality of elemental patterns arranged in a direction of a given straight line, the aberration measuring pattern units being disposed in a given circumferential direction such that the straight line of each of the aberration measuring pattern units is cyclically shifted relative to a reference line at an angle of (xcfx80/2)/(2n+1) rad (n=natural number) in a range between 0 rad and xcfx80/2 rad. Thereby, third- or more-order aberrations, other than in the axial direction, which could be not be measured in the prior art, can be measured.
Additional objects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out hereinafter.